Differential Equations and Boundary Value Problems Computing and Modeling

ISBN-10: 0130652458
ISBN-13: 9780130652454
Edition: 3rd 2004 (Revised)
List price: $144.20
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Description: For introductory courses in Differential Equations. This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualization of a modern differential  More...

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Book details

List price: $144.20
Edition: 3rd
Copyright year: 2004
Publisher: Prentice Hall PTR
Publication date: 6/18/2003
Binding: Hardcover
Pages: 727
Size: 8.50" wide x 10.25" long x 1.00" tall
Weight: 3.586
Language: English

For introductory courses in Differential Equations. This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances the traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

Application Modules
Preface
First-Order Differential Equations
Differential Equations and Mathematical Models
Integrals as General and Particular Solutions
Slope Fields and Solution Curves
Separable Equations and Applications
Linear First-Order Equations
Substitution Methods and Exact Equations
Mathematical Models and Numerical Methods
Popuiation Models
Equilibrium Solutions and Stability
Acceleration-Velocity Models
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method
The Runge-Kutta Method
Linear Equations of Higher Order
Introduction: Second-Order Linear Equations
General Solutions of Linear Equations
Homogeneous Equations with Constant Coefficients
Mechanical Vibrations
Nonhomogeneous Equations and Undetermined Coefficients
Forced Oscillations and Resonance
Electrical Circuits
Endpoint Problems and Eigenvalues
Introduction to Systems of Differential Equations
First-Order Systems and Applications
The Method of Elimination
Numerical Methods for Systems
Linear Systems of Differential Equations
Matrices and Linear Systems
The Eigenvalue Method for Homogeneous Systems
Second-Order Systems and Mechanical Applications
Multiple Eigenvalue Solutions
Matrix Exponentials and Linear Systems
Nonhomogeneous Linear Systems
Nonlinear Systems and Phenomena
Stability and the Phase Plane
Linear and Almost Linear Systems
Ecological Models: Predators and Competitors
Nonlinear Mechanical Systems
Chaos in Dynamical Systems
Laplace Transform Methods
Laplace Transforms and Inverse Transforms
Transformation of Initial Value Problems
Translation and Partial Fractions
Derivatives, Integrals, and Products of Transforms
Periodic and Piecewise Continuous Input Functions
Impulses and Delta Functions
Power Series Methods
Introduction and Review of Power Series
Series Solutions Near Ordinary Points
Regular Singular Points
Method of Frobenius: The Exceptional Cases
Bessel's Equation
Applications of Bessel Functions
Fourier Series Methods
Periodic Functions and Trigonometric Series
General Fourier Series and Convergence
Fourier Sine and Cosine Series
Applications of Fourier Series
Heat Conduction and Separation of Variables
Vibrating Strings and the One-Dimensional Wave Equation
Steady-State Temperature and Laplace's Equation
Eigenvalues and Boundary Value Problems
Sturm-Liouville Problems and Eigenfunction Expansions
Applications of Eigenfunction Series
Steady Periodic Solutions and Natural Frequencies
Cylindrical Coordinate Problems
Higher-Dimensional Phenomena
References for Further Study
Existence and Uniqueness of Solutions
Answers to Selected Problems
Index

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